While racing on a flat track, a car rounds a curve of 56 m radius and instantaneously experiences a centripetal acceleration of 36 m/s2. How fast was the car going?

I know the answer i s45 I just need to know why ASAP!!!!!!!!!!!!!!!!!!!!

a = v^2/r

ar = v^2
56*36 = v^2
2016 = v^2
v = 44.9

To determine how fast the car was going, we can use the formula for centripetal acceleration:

a = (v^2) / r

Where:
- a is the centripetal acceleration
- v is the velocity of the car
- r is the radius of the curve

We are given that the centripetal acceleration is 36 m/s^2, and the radius of the curve is 56 m. We need to find the velocity.

Rearranging the formula, we get:

v^2 = a * r

Substituting the given values:

v^2 = 36 m/s^2 * 56 m

Now we can solve for v by taking the square root of both sides:

v = √(36 m/s^2 * 56 m)

v ≈ 45 m/s

Therefore, the car was going approximately 45 m/s.

To find the speed at which the car was going while rounding the curve, we can use the formula for centripetal acceleration:

a = (v^2) / r

Where:
a = centripetal acceleration (given as 36 m/s^2)
v = speed of the car
r = radius of the curve (given as 56 m)

Rearranging the formula to solve for v:

v = sqrt(a * r)

Plugging in the given values:

v = sqrt(36 * 56)

v = sqrt(2016)

v ≈ 44.9 m/s

Therefore, the speed of the car was approximately 44.9 m/s or rounded to the nearest whole number, 45 m/s.